With the miniaturization of semiconductor devices in recent years, the reduction in the wavelength of an exposure light source for use in the photolithography technique has been proceeding. In the advanced transmission photolithography field, an ArF excimer laser (wavelength 193 nm) with a wavelength of 200 nm or less is used as an exposure light source. However, a demand for further miniaturization has been increasing and such a demand is difficult to satisfy only by using the ArF excimer laser light as the exposure light source. In order to satisfy the demand, an increase of NA (numerical number) has been adopted by using the oblique illumination method or the like. With the increase in NA, however, the focal depth of an exposure apparatus has been decreasing significantly. As a consequence, when a transfer mask is set (chucked) to the exposure apparatus by vacuum suction or the like, if the transfer mask is deformed to reduce its flatness as compared with that before the setting (chucking), focus positions may be often deviated on transferring a mask pattern of the transfer mask onto a semiconductor substrate as a transfer object. Thus, the transfer accuracy has been degraded.
In view of this, it has been proposed to simulate, using the finite element method, a shape of a transparent substrate for use in a mask blank when the transparent substrate is set in an exposure apparatus, thereby estimating a flatness thereof.
However, there has been a problem that, although the shape of a main surface of the substrate can be estimated somewhat accurately by the simulation of the substrate shape using the finite element method, the simulation is very time-consuming.
In the DRAM hp32 nm and subsequent generations, it has been studied to use the double patterning technique. The double patterning technique is to divide a single fine high-density pattern into two relatively coarse patterns, to produce transfer masks for the two patterns, respectively, and to form a fine high-density pattern on an object using these two transfer masks. As the double patterning technique, there have been proposed several techniques such as the double exposure technique, the narrow-sense double patterning technique, the technique using a spacer, and the technique using resist freezing. However, these techniques are common in carrying out two-time exposure processes using two transfer masks to thereby form a single fine high-density pattern. That is, two transfer masks are not simultaneously used in a one-time exposure process, but a process of chucking a transfer mask on a mask stage of an exposure apparatus and irradiating exposure light onto the transfer mask to transfer a transfer pattern is carried out per transfer mask. Accordingly, the positioning accuracy of two patterns should be significantly enhanced than conventional. As a consequence, there has arisen a need to design a transfer pattern to be formed in each transfer mask by taking into account also the position offset of the pattern that occurs when the transfer mask is chucked on the mask stage of the exposure apparatus.
In view of this, it is now being studied to correct a transfer pattern using simulation results of a substrate shape when writing the transfer pattern on a photoresist-coated mask blank, and to write a corrected transfer pattern in the course of the manufacture of an exposure mask (e.g. Non-Patent Document 1).